Degrees of freedom, equipartition and specific heats — NEET & JEE Questions

Question 1 · difficulty L1 · recall

According to equipartition, each independent quadratic degree of freedom contributes an average energy of

• A. $\frac12 k_BT$
• B. $k_BT$
• C. $2k_BT$
• D. $\frac14 k_BT$

Question 2 · difficulty L2 · understanding

The internal energy of air in $4 \mathrm{~m} \times 4 \mathrm{~m} \times 3 \mathrm{~m}$ sized room at 1 atmospheric pressure will be___________________$\times 10^6 \mathrm{~J}$ (Consider air as diatomic molecule)

Question 3 · difficulty L2 · understanding

The total internal energy of two mole monoatomic ideal gas at temperature T = 300 K will be _____________ J. (Given R = 8.31 J/mol.K)

Question 4 · difficulty L2 · understanding

If 2 mole of an ideal monoatomic gas at temperature $T$, is mixed with 6 mole of another ideal monoatomic gas at temperature $2 T$ then the temperature of mixture is:

• A. $\frac{5}{2} T$
• B. $\frac{5}{4} T$
• C. $\frac{7}{2} T$
• D. $\frac{7}{4} T$

Question 5 · difficulty L2 · understanding

Match the List I with List II List - I List - II (A) Triatomic rigid gas (I) $\frac{C_p}{C_v}=\frac{5}{3}$ (B) Diatomic non-rigid gas (II) $\frac{C_p}{C_v}=\frac{7}{5}$ (C) Monoatomic gas (III) $\frac{C_p}{C_v}=\frac{4}{3}$ (D) Diatomic rigid gas (IV) $\frac{C_p}{C_v}=\frac{9}{7}$ Choose the correct answer from the options given below:

• A. A-III, B-IV, C-I, D-II
• B. A-II, B-IV, C-I, D-III
• C. A-IV, B-II, C-III, D-I
• D. A-III, B-II, C-IV, D-I

Question 6 · difficulty L2 · understanding

A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature $$(27^{\circ} \mathrm{C})$$. The ratio of specific heat of gases at constant volume respectively is:

• A. $$\frac{3}{2}$$
• B. $$\frac{3}{5}$$
• C. $$\frac{7}{5}$$
• D. $$\frac{5}{3}$$

Question 7 · difficulty L2 · understanding

The translational degrees of freedom $$\left(f_t\right)$$ and rotational degrees of freedom $$\left(f_r\right)$$ of $$\mathrm{CH}_4$$ molecule are:

• A. $$f_t=2$$ and $$f_r=2$$
• B. $$f_t=3$$ and $$f_r=3$$
• C. $$f_t=3$$ and 4$f_r=2$$
• D. $$f_t=2$$ and $$f_r=3$$

Question 8 · difficulty L2 · understanding

Two moles a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is :

• A. $\frac{3}{2} \mathrm{R}$
• B. $\frac{7}{4} \mathrm{R}$
• C. $\frac{5}{2} \mathrm{R}$
• D. $\frac{9}{4} \mathrm{R}$

Question 9 · difficulty L2 · understanding

The mean free path of molecules of a certain gas at STP is $$1500 \mathrm{~d}$$, where $$\mathrm{d}$$ is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at $$373 \mathrm{~K}$$ is approximately:

• A. $$750 \mathrm{~d}$$
• B. $$1500 \mathrm{~d}$$
• C. $$\mathrm{2049~ d}$$
• D. $$1098 \mathrm{~d}$$

Question 10 · difficulty L2 · understanding

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafloride (polyatomic). Arrange these on the basis of their root mean square speed $$\left(v_{\mathrm{rms}}\right)$$ and choose the correct answer from the options given below:

• A. $$\mathrm{v}_{\mathrm{rms}}($$ mono $$)=\mathrm{v}_{\mathrm{rms}}($$ dia $$)=\mathrm{v}_{\mathrm{rms}}($$ poly $$)$$
• B. $$\mathrm{v}_{\mathrm{rms}}$$ (mono) $$> \mathrm{v}_{\mathrm{rms}}($$ dia $$) > \mathrm{v}_{\mathrm{rms}}$$ (poly)
• C. $$\mathrm{v}_{\mathrm{rms}}$$ (dia) $$< \mathrm{v}_{\mathrm{rms}}$$ (poly) $$< \mathrm{v}_{\text {rms }}$$ (mono)
• D. $$\mathrm{v}_{\mathrm{rms}}$$ (mono) $$< \mathrm{v}_{\mathrm{rms}}$$ (dia) $$< \mathrm{v}_{\mathrm{rms}}$$ (poly)